Answer to Question #163017 in Statistics and Probability for Sunny

Question

If the variables x resembles same as variable Y, then the covariance between the two variables reduces to:

a. the covariance of either variables

b. the correlation of either variables

c. the standard deviation of either variables

d. the variance of either variables

e. the expected value of either variables

Answer 1

We know that generally covariance of the two variable $X$ and $Y$ lies between [-1, 1]

$|Cov(X,Y)| \leq \sqrt{V_{ar}(X)V_{ar}(Y)}$

But we know that $V_{ar}(X)=V_{ar}(Y)$

Hence, we can conclude that

$|Cov(X,Y)|\leq Var(X)$

so d is the correct answer.